Graph Transformations of Parent Functions

This worksheet is an inquiry-based activity used to explore the effects of graph transformations on various parent functions.

Part 1
Type x^2 into the input box and press enter.
Click the yellow button to explore the graph of g(x)=a*f(x).
Move the slider to change the value of a.
Make a conjecture about how the value of a transforms the graph of f(x) to the graph of g(x).
Repeat the same work with the following functions and test your conjecture.
x3 (type x^3)
|x| (type abs(x))
√x (sqrt(x))
Does your conjecture hold? If not change it.
Does your conjecture hold if 0<a<1? If not, modify it.
Does your conjecture still hold if a < 0? If not, modify it.
Does your conjecture still hold if a = 0? If not, modify it.
Part 2.
Type x^2 into the input box and press enter.
Click the green button to explore the graph of g(x)=f(x-h).
Move the slider to change the value of h.
Your task consists of making a conjecture about how the value of h transforms the parent function.
Observe the transformations of the graph with the changes of the value h.
Do the same using the following functions: x3 (type x^3) ; |x| (type abs(x)); and √x (sqrt(x))
Based upon your observations, make a conjecture on how the value of “h” affects the graph of the equation g(x)=f(x-h).
Does your conjecture hold for h>0? If not, modify your conjecture.
Does your conjecture hold for h<0? If not, modify your conjecture.
Part 3.
Type x^2 into the input box and press enter.
Click the blue button to explore the graph of g(x)=f(x)+k.
Move the slider to change the value of k.
Your task consists of making a conjecture about how the value of k transforms the parent function.
Observe the transformations of the graph with the changes of the value k.
Do the same using the following functions: x3 (type x^3) ; |x| (type abs(x)); and √x (sqrt(x))
Based upon your observations, make a conjecture on how the value of “h” affects the graph of the function g(x)=f(x)+k.
Does your conjecture hold for k>0? If not, modify your conjecture.
Does your conjecture hold for k<0? If not, modify your conjecture.
Part 4
Type x^2 into the input box and press enter.
Click the red button to explore the graph of g(x)=a*f(x-h)+k.
Move the sliders to change the values of a, h, and k.
Observe how each of these values transforms the five parent functions and check the conjectures you have made.